Model3D#

class timflow.steady.model.Model3D(kaq=1, z=None, kzoverkh=1, npor=0.3, topboundary='conf', topres=0, topthick=0, hstar=0)#

Bases: Model

Create a multi-layer model object consisting of stacked aquifer layers.

The resistance between the layers is computed from the vertical hydraulic conductivity of the layers.

Parameters:

kaq (float, array or list) – hydraulic conductivity of each layer from the top down if float, hydraulic conductivity is the same in all aquifers
z (array or list) – elevation of top of system followed by bottoms of all layers from the top down bottom of layer is automatically equal to top of layer below it length is number of aquifer layers + 1
kzoverkh (float) – vertical anisotropy ratio vertical k divided by horizontal k if float, value is the same for all layers length is number of layers
npor (float, array or list) – porosity of all aquifer layers from the top down if float, porosity is the same for all layers if topboundary=’conf’: length is number of layers if topboundary=’semi’: length is number of layers + 1
topboundary (string, 'conf' or 'semi' (default is 'conf')) – indicating whether the top is confined (‘conf’) or semi-confined (‘semi’)
topres (float) – resistance of top semi-confining layer (read if topboundary=’semi’)
topthick (float) – thickness of top semi-confining layer (read if topboundary=’semi’)
hstar (float or None (default is None)) – head value above semi-confining top (read if topboundary=’semi’)

Notes

For semi-confined aquifers, set top equal to ‘semi’ and provide:

topres: resistance of top
tophick: thickness of top
hstar: head above top

Examples

Create a 3D model with 10 layers:

ml = Model3D(kaq=10, z=np.arange(20, -1, -2), kzoverkh=0.1)

remove_element(e)#: Remove element e from model.

disvec(x, y, aq=None)#

Discharge vector at x, y.

Returns:: qxqy – first row is Qx in each aquifer layer, second row is Qy
Return type:: array size (2, naq)

normflux(x, y, theta)#

Flux at point x, y in direction of angle theta.

Parameters:

x (float)
y (float)
theta (float) – angle for which to calculate flux, defined relative to positive x-axis.

Returns:

flux in direction theta

Return type:

flux

intnormflux_segment(x1, y1, x2, y2, method='legendre', ndeg=10)#

Integrated normal (perpendicular) flux over specified line segment.

Flux to the left is positive when going from (x1, y1) to (x2, y2).

Parameters:

x1 (float)
y1 (float)
x2 (float)
y2 (float)
method (str, optional) – integration method, either “quad” (numerical integration using scipy) or “legendre” (approximate integral using Gauss-Legendre quadrature), by default “legendre”.
ndeg (int, optional) – degree for legendre polynomial, by default 10, only used when method=”legendre”

Returns:

Qn – integrated normal flux along specified line

Return type:

np.array

intnormflux(xy, method='legendre', ndeg=10)#

Integrated normal (perpendicular) flux over polyline.

Computes the flux per segment and per aquifer. Flux to the left is positive when going from (x1, y1) to (x2, y2).

Parameters:

xy (list [(x0, y0), (x1, y1),... , (xn, yn)] or 2D array) – if 2D-array, x in first column and y in second column
method (str, optional) – integration method, either “quad” (numerical integration using scipy) or “legendre” (approximate integral using Gauss-Legendre quadrature), by default “legendre”.
ndeg (int, optional) – degree for legendre polynomial, by default 10, only used when method=”legendre”

Returns:

Qn – integrated normal flux along specified polyline

Return type:

np.array of shape (naq, nsegments)

Examples

Total flow across polyline can be obtained using:

>>> np.sum(Qn)

Total flow across segments summed over aquifers using

>>> np.sum(Qn, axis=0)

head(x, y, layers=None, aq=None)#

Head at x, y.

Returns:: h – head in all layers (if not None), or all layers of aquifer (otherwise)
Return type:: array length naq or len(layers)

head_array(x, y, layers=None, show_progress=False, parallel=False)#

Head for array of points.

Parameters:

x (1D array or list) – x values of points
y (1D array or list) – y values of points
layers (integer, list or array, optional) – layers for which grid is returned
show_progress (bool) – show computation progress, by printing dots per row or with tqdm progressbar when parallel is True. Default is False.
parallel (bool or int, optional) – if True, computes head_array in parallel using multiprocessing, by default False. If an integer is provided, it is interpreted as the number of processes to use.

Returns:

h – heads array with size (nlayers, npoints)

Return type:

array

headgrid(xg, yg, layers=None, printrow=False, show_progress=False, parallel=False)#

Grid of heads.

Parameters:

xg (1d-array) – x values of grid
yg (1d-array) – y values of grid
layers (integer, list or array, optional) – layers for which grid is returned
show_progress (bool) – show computation progress, by printing dots per row or with tqdm progressbar when parallel is True. Default is False.
parallel (bool or int, optional) – if True, computes headgrid in parallel using multiprocessing, by default False. If an integer is provided, it is interpreted as the number of processes to use.
printrow (bool, optional) –

Deprecated since version 0.2.0: prints dot to screen for each row of grid if set to True

Returns:

h

Return type:

array size nlayers, ny, nx